Dark Breathers in Granular Crystals

Abstract

We present a study of the existence, stability and bifurcation structure of families of dark breathers in a one-dimensional uniform chain of spherical beads under static load. A defocus- ing nonlinear Schrodinger equation (NLS) is derived for frequencies that are close to the edge of the phonon band and is used to construct targeted initial conditions for numerical computations. Salient features of the system include the existence of large amplitude solutions that bifurcate with the small amplitude solutions described by the NLS equation, and the presence of a nonlinear instability that, to the best of the authors knowledge, has not been observed in classical Fermi- Pasta-Ulam lattices. Finally, it is also demonstrated that these dark breathers can be detected in a physically realistic way by merely actuating the ends of an initially at rest chain of beads and inducing destructive interference between their signals.

References in corpus (4)

• Intrinsic Energy Localization through Discrete Gap Breathers in One-Dimensional Diatomic Granular Crystals
• Discrete breathers in Fermi-Pasta-Ulam lattices
• Bright and dark breathers in Fermi-Pasta-Ulam lattices
• Variational approximations for travelling solitons in a discrete nonlinear Schrödinger equation

Cited by in corpus (12)

• Nonlinear Coherent Structures in Granular Crystals
• Damped-Driven Granular Crystals: An Ideal Playground for Dark Breathers and Multibreathers
• Superdiffusive Transport and Energy Localization in Disordered Granular Crystals
• Breathers in a locally resonant granular chain with precompression
• Phononic Rogue Waves
• Dynamics of Time-Modulated, Nonlinear Phononic Lattices
• Bright Breathers in Nonlinear Left-Handed Metamaterial Lattices
• Nonlinear waves in a strongly nonlinear resonant granular chain
• Linear and nonlinear dynamics of isospectral granular chains
• Breathers in lattices with alternating strain-hardening and strain-softening interactions
• Breather modes of fully nonlinear mass-in-mass chains
• Limiting Phase Trajectories: a new paradigm for the study of highly non-stationary processes in Nonlinear Physics